Encyclopedia of Microtonal Music Theory

3/4-tone, three-quarter-tone

1. Approximate musical interval

Any interval intermediate between the Half Tone and the Whole Tone. [In just ratios,] Three-Quarter Tones range from about 13/12 (139 cents [¢]) to 11/10 (165¢).

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[Joe Monzo]

2. One degree of 8-edo

Calculated as the 8th root of 2 -- 8√2, or 2(1/8) -- an irrational proportion with the approximate ratio of 1 : 1.090507733, and an interval size of exactly 150 cents. It is the size of one degree, and thus the basic "step" size, in the 8-edo (or 8-tET) scale.

The 3/4-tone occurs in all divisions of the octave which are multiples of 8 -- thus, it is a significant feature of the popular 24-edo quarter-tone scale, in which it traverses a pitch space of 3 degrees.

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